Matrix driving method for electro-optical display device

ABSTRACT

A matrix driving method for driving an electro-optical display device including digit and segment electrodes arranged in a matrix configuration, in which digit and segment drive signals are applied to digit and segment electrodes in such a manner that the digit drive signals applied to all the digit electrodes have potentials equal in level with each other during a prescribed time interval during which the potential of a first segment drive signal inducing a state of non-display at all the digit electrodes is equal to the potential of each of the digit drive signals. During the prescribed time intervals, the potential difference between a second segment drive signal inducing a state of display at one of the digit electrodes and a state of non-display at the other digit electrode and each of the digit drive signals is maintained in a first predetermined value whereby the root mean square value of the potential difference between the second segment drive signal and the digit drive signal applied to the other digit electrode is substantially equal to that of the potential difference between the first segment drive signal and each of the digit drive signals. During the prescribed time interval, further, the potential difference between a third segment drive signal inducing a state of display at all the digit electrodes and each of the digit drive signals is maintained in a second predetermined value whereby the root mean square value of the potential difference between the second segment drive signal and the digit drive signal applied to the one of the digit electrodes is substantially equal to that of the potential difference between the third segment drive signal and each of the digit drive signals.

This application is a continuation in part of patent application Ser. No. 784,746, filed Apr. 5, 1977, now abandoned.

This invention relates to a method for driving an electro-optical display device such as a liquid crystal display device and, more particularly, to a method for driving an electro-optical display device having digit and segment electrodes arranged in a matrix configuration.

In recent years, electro-optical display devices such as liquid crystal display devices have been increasingly used in various applications such as electronic timepieces, desk calculators, etc., because of low power consumption. It is known in the art that there are two types of arrangements for the electrodes of the liquid crystal display devices, i.e., a static type arrangement and a matrix type arrangement. In the static type arrangement, the liquid crystal display device comprises a common electrode and a plurality of groups of segment electrodes displaced from and disposed opposite the common electrode. The segment electrodes of each group are not interconnected and independently driven from each other. This arrangement is advantageous in that a driver circuit for each segment electrode can be manufactured in a simple construction. However, this has drawbacks in that a number of driver circuits are required and increases the number of leads from the liquid crystal display device, increasing packaging cost and complexity.

In the matrix type arrangement, the liquid crystal display device comprises a plurality of digit electrodes, and a plurality of segment electrodes displaced from and disposed opposite all of the digit electrodes. The segment electrodes relative to each digit electrode are interconnected, and the digit electrodes are provided independently from each other. Generally, the digit electrodes are driven in a time multiplexed relationship. With this arrangement, the number of leads from the liquid crystal display device is remarkably reduced, representing a considerable saving in packaging cost and complexity. However, this suffers from drawbacks in the design of driver circuits because of low display contrast.

It is, therefore, an object of the present invention to provide a method for driving an electro-optical display device in a matrix mode which can overcome the shortcomings encountered in the prior art.

It is another object of the present invention to provide a driving method for driving an electro-optical display device in a matrix mode so as to provide a remarkably increased operation margin to increase display contrast.

These and other, objects, features and advantages of the present invention will become more apparent from the following description when taken in conjunction with the accompanying drawings, in which:

FIG. 1A is an example of a timing chart for an example of a conventional drive signal to be used for driving an electro-optical display device;

FIG. 1B is a vector diagram of the drive signal shown in FIG. 1A;

FIG. 2 is a schematic view of an example of a conventional electro-optical display device arranged in a matrix configuration;

FIG. 3 is a timing chart for illustrating another example of conventional digit and segment drive signals to be used for driving the display device shown in FIG. 2;

FIG. 4 is a timing chart of another example of conventional digit and segment drive signals;

FIG. 5 shows vector diagrams for the drive signals shown in FIG. 4;

FIG. 6 is a timing chart for another example of conventional drive signals;

FIG. 7 is a timing chart for illustrating the potential differences across the electrodes of the display device;

FIG. 8 is a timing chart for another example of prior art drive signals;

FIG. 9 is a timing chart for illustrating a prior art concept of the method of the present invention;

FIG. 10 shows vector diagrams for the drive signals shown in FIG. 9;

FIG. 11 is a timing chart for a preferred example of digit and segment drive signals used in a method of the present invention;

FIG. 12 shows the potential differences across the electrodes applied with the drive signals shown in FIG. 11;

FIG. 13 shows vector diagrams for the drive signals shown in FIG. 11;

FIG. 14 is a timing chart for another preferred example of digit and segment drive signals according to the present invention;

FIG. 15 shows the potential difference across the electrodes applied with the drive signals shown in FIG. 14;

FIG. 16 is a timing chart for another preferred example of digit and segment drive signals according to the present invention;

FIG. 17 is a vector diagram for one of the drive signals shown in FIG. 16;

FIG. 18 shows the potential differences across the electrodes applied with the drive signals shown in FIG. 17;

FIG. 19A is a timing chart for another preferred example of digit and segment drive signals according to the present invention;

FIG. 19B is a schematic view of an example of an electro-optical display device arranged in a matrix configuration for the digit and segment drive signals shown in FIG. 19A;

FIG. 20 shows the potential differences across the electrodes applied with the drive signals shown in FIG. 19;

FIG. 21 shows the vector diagrams for the drive signals shown in FIG. 19;

FIG. 22 is a timing chart for another preferred example of digit and segment drive signals according to the present invention;

FIG. 23 is a block diagram of an example of a driver circuit to carry out a method of the present invention;

FIG. 24 is a view showing an example of an arrangement of a display device shown in FIG. 23;

FIG. 25 is a detail circuitry for a timing pulse generator shown in FIG. 23;

FIG. 26 is a timing chart for timing signals generated by the circuit shown in FIG. 25;

FIG. 27 is a detail circuitry for a segment signal generator shown in FIG. 23;

FIG. 28 is a detail circuitry for a segment driver shown in FIG. 23;

FIG. 29 is a detail circuitry for a digit driver shown in FIG. 23;

FIG. 30 is a graph illustrating voltage characteristics for a liquid crystal;

FIG. 31 shows graphs illustrating voltage-contrast curves for a liquid crystal when driving is accomplished by a driving method according to the present invention; and

FIG. 32 shows diagrams illustrating the relationship between the potential levels and the drive signals used in a driving method of the present invention.

Before entering to a detailed description of the present invention, an explanation will be given to how to convert a potential of a driving signal to vector quantities with reference to FIGS. 1A and 1B. A signal cycle or half cycle T of the driving signal waveform is divided into a number of intervals t₁, t₂, . . . t_(j). t_(i) is assumed as the width (duration) of the i-th interval, and the potential of the driving signal over each such interval is assumed to be constant and is assigned as e_(i). The j-dimension vector e having the i-th component which specified e_(i) √t_(i) /T will be herein defined as a vector corresponding to the driving waveform E (FIG. 1) and expressed in the following equation: ##EQU1## FIG. 1B shows the vector diagram indicating the components of the vector e. FIGS. 1A and 1B shows examples of the waveforms of the driving signal and the vector diagram in which j=3.

The root mean square value V_(k1) of the potential representative of the difference between two signals A_(k) and A_(I) becomes: ##EQU2##

This is equivalent to the distance between a_(k) and a₁ in the j-dimension space, namely ##EQU3##

The signal waveforms A₁, A₂, . . . A_(n) may be brought into correspondence with another set of vectors a₁ ', a₂ ', . . . a_(n) ' by an interval dividing method which is different from that given above. These vectors may be different from a₁, a₂, . . . a_(n) even in dimension number, but a₁, a₂, . . . a_(n) and a₁ ', a₂ ', . . . a_(n) ' are congruent. In other words, it is possible to bring them into coincidence by rotational movement, parallel movement and a reversal transformation.

The transformation from vectors a₁, a₂, . . . a_(n) to signal waveforms will be carried out by a procedure which is the reverse of that stated above. However, this transformation is not a one-to-one correspondence because in this case t₁, t₂, . . . t_(n) can be arbitrarily selected according to formula (1).

However, when the method of selecting t₁, t₂, . . . t_(n) is changed and a transformation made to other signals A₁ ', A₂ ', the root mean square values of the potential differences between signals, that is signals A₁, A₂, . . . A_(n) and signals A₁ ', A₂ ', . . . A_(n) ', maintain the same relation. The root mean square value of the potential differences also maintain the same relation for A₁ ", A₂ ", . . . A_(n) " in which a transformation is made to signal waveforms from vectors a₁ ', a₂ ', . . . a_(n) ', obtained by the rotational movement, parallel movement and reverse transformation of vectors a₁, a₂, . . . a_(n). Accordingly, it can be understood that signal waveform groups A₁, A₂, . . . A_(n) ; A₁ ', A₂ ', . . . A_(n) '; and A₁ ", A₂ ", . . . A_(n) " constitute components of one set A. Likewise, a₁, a₂, . . . a_(n) and a₁ ', a₂ ' . . . a_(n) ' constitute components of one set a over the vector space, with which set A may be considered to be in one-to-one correspondence.

Considering the transformation from vector to waveform in a practical light, it is preferable that the waveform be as simple as possible; in particular, the simplicity of the signal waveform has a great effect upon the number of gates in the driving circuit. It follows that there are cases in which prior to transforming the vectors it is better to perform a suitable transformation of coordinates to change the vector dimension number before making the transformation to the waveforms.

A convenient method of dealing with the transformation of vector coordinates is to apply a matrix as shown below. For a transformation from j-dimension vectors a₁, . . . a_(n) to l-dimension vectors a'₁, . . . a'_(n), we have ##EQU4##

Vectors a_(n), a'_(n) are thus represented respectively by matrix with j rows and l rows, and (a'₁, a'₂ . . . a'_(n)) with l rows and n columns are represented by the following matrix: ##EQU5##

Assume that K represents a matrix with l rows and n columns. To represent a unit matrix I with l rows and l columns, use is made of a matrix N with l rows and n columns where N^(T) ·N=I so that (a₁ ', a₂ ', . . . a_(n) ')=N·(a₁, a₂ . . . a_(n))+K

Referring now to FIG. 2, there is shown a model matrix layout in which the i order represents a group of digit electrodes while the j order denotes a group of segment electrodes. Discussion will now be directed toward the relationships between digit driving signals and address signals applied to the j segment electrodes.

FIG. 3 shows typical voltage waveforms which are applied in the prior art to the digit and segment electrodes. Discussion will be made with respect to one-half the driving period. In FIG. 3, ±d will be taken as the voltage impressed upon the digit electrodes while ±s represents the voltage impressed upon the segment electrodes. In FIG. 3, reference numeral 10 denotes the waveform of the voltage applied to the i-th digit electrode and reference numeral 12 the waveform of the voltage applied to the (i+m)-th digit electrode. Reference numeral 14 denotes the waveform of the voltage impressed upon segment electrode j.

Hereinafter the matrix driving system will be described, using an integer n representing a n digits (n≦2). In general, the timing relationship between waveforms 10 and 12 will be assumed as follows: the portion denoted by reference numeral 10' will be represented by 1/n and the portion 10" by (n-i)/n. In other words, n represents the number of the digit electrodes and 1/n the duty.

FIGS. 3(4) and 3(5) represent the voltage difference between the electrodes. Here, reference numeral 16 denotes the voltage waveform for an intersection i.j, and 18 the voltage waveform for an intersection (i+m).j. To obtain the root mean square (rms) voltage of the waveform shown in FIG. 3(4), the following equation is employed: ##EQU6## while the equation for the rms voltage of the waveform in FIG. 3(5) is given by ##EQU7## where (4) denotes a display state and (5) a non-display state. Letting s=1, the operation margin α can be obtained from ##EQU8## The operation margin is thus the value which represents the minimum ratio of the rms voltage during a period in which there is a display to the rms voltage during a period in which there is no display; accordingly, the values of n and d determine the operation margin. It follows then that when driving a 2-digit matrix with n=2, α=√5 for d=1 and for d=2. When d=1, this corresponds to so-called 1/2 biasing whereas 1/3 biasing corresponds to a case where d=2. From the above equation (2) it will be seen that when d=√n, the operation margin α becomes the maximum value, i.e., ##EQU9##

It is apparent from the above description that in a conventional system the maximum operation margin is (√2+1) for matrix driving with n=2. Such systems are premised on the fact that there is no overlapping of phases or potential levels with regard to the signals which drive the respective digits.

FIG. 4 shows the waveform diagrams for the driving signals to be applied to digit and segment electrodes in various prior art driving methods in which n=2, and FIG. 5 shows vector diagrams for the signals shown in FIG. 4. In FIG. 4, r₁ represents the waveform impressed upon a first digit electrode, and r₂ the waveform impressed upon a second digit electrode. Similarly, c₀ represents the waveform impressed upon a segment electrode to induce a non-display state at intersections between the segment electrode and both the first and second digit electrodes. C₁₂ represents the waveform by which the segments at both the corresponding intersections are in a state of display. Similarly, C₁ is the waveform by which the segment at an intersection with the first digit electrode and the second digit electrode is in state of non-display. FIG. 4(1) represents a group of waveforms for the driving signals in the 1/2 biasing method in which V_(r) =V_(c). FIG. 4(2) represent the waveform for the driving signals in the 1/3 biasing method in which V_(r) =2 V_(c). Similarly, FIG. 4(3) represents the waveforms for the driving signals in which V_(r) =√2·V_(c).

In FIG. 5(1), a convenient set of X and Y axes is chosen and r₁ and r₂ indicative of varying potentials of corresponding digit drive signals r₁ ' and r₂ ' are resolved as vectors into X and Y components along these axes. In FIG. 5(1), the symbols C₀, C₁ and C₁₂ represent varying potentials of the corresponding segment drive signals C₀, C₁ and C₁₂. The symbol G represents the mean value in potential of the digit drive signals at each time instant. The time interval t₁ is resolved into the X axis, and the time interval t₂ is resolved into the Y axis. In FIG. 5(1), r₁ has a potential value of 1 during the time interval t₁, and r₂ has a potential value of 0 during the time interval t₂. Similarly, r₂ has a value of 0 during the time interval t₁ and has a value of 1 during the time interval t₂. Resolving c₀ at co-ordinates (1, 1), c₁ at co-ordinates (-1, 1), c₂ at co-ordinates (1, -1) and c₁₂ at co-ordinates (-1, -1) produces a square with the length of each side having a potential value of 2. G is plotted at co-ordinates (1/2, 1/2). Vector a represents the rms voltage V_(off) indicative of the state of non-display, and vector b represents the rms voltage V_(on) indicative of the state of display. Since the operation margin α is expressed by the ratio of V_(on) to V_(off), the following equation holds:

    α=|b|/|a|=√5/1=√5

In a case shown in FIG. 5(2), G is plotted at the same point as C₀, and |a|=√2 and |b|=√10. Therefore, the operation margin α is √5. Similarly, in a case of FIG. 5(3) G is plotted at a point (√2/2, √2/2). In this example, since |a|=2(2-√2) and |b|=2(2+√2), the operation margin α is 1+√2.

The relationship in the three cases among r₁, r₂, c₀, c₁, c₂ and c₁₂ with respect to the half period is expressed by the following matrixes: ##EQU10##

FIGS. 6 (1, 2, 3) shows the actual waveforms for the situation described with reference to FIG. 4(2), i.e., with n=2, Vc=1 and Vr=2. FIG. 6(1) shows the waveform impressed upon a digit electrode D1, and FIG. 6(2) shows the waveform impressed upon a digit electrode D2. Similarly, FIG. 6(3) shows the waveform impressed upon any segment electrode Sj to display only in the digit D1. As may be appreciated from the drawings, five potential levels, namely 0, Vo, 2 Vo, 3 Vo and 4 Vo are employed. By combining these waveforms a liquid crystal may be driven at an operational margin of √5.

FIGS. 6(4), (5) and (6) correspond as in FIG. 4(1) to a case in which Vc=Vr=1 and show the waveforms which are impressed upon a digit electrode D1, a digit electrode D2, and any segment electrode Sj to display only in the digit D1, respectively. As previously explained, the obtainable operation margin α is √5. Here, three potentials 0, Vo and 2 Vo are employed.

FIG. 7 illustrates the waveforms which are obtained across the electrodes of a liquid crystal by making use of the waveforms shown in FIG. 6. FIG. 7(1) shows the waveforms for a display state when Vr=2, and FIG. 7(2) the waveforms for a non-display state when Vr=2. Similarly, FIGS. 7(3) and (4) depict the respective waveforms for display and non-display states when Vr=1.

FIG. 8 depicts the waveforms for matrix driving in accordance with conventional systems when n=2 and four potentials, namely 0, Vo, 2 Vo and 3 Vo are employed. FIGS. 8(1) and (2) show the waveforms which are impressed upon a digit electrode D1 and a digit electrode D2, respectively. It can be understood from FIG. 8(1) that the driving signal for these digit electrodes consists of four equal intervals t₁, t₂, t₃ and t₄ which comprise one period (or cycle time). If the potentials for the D1 digit signal and D2 digit signal over each of these intervals are added, the sums are 4 Vo for t₁, 2 Vo for t₂, 4 Vo for t₃ and 2 Vo for t₄, thus repetitively alternating between 4 Vo and 2 Vo. In other words, either a potential of 0 or 3 Vo appears once during each unit time interval without overlapping each another and at no time do identical potential levels appear during any of the intervals t₁ through t₄.

FIGS. 8(3), (4), (5) and (6) show the waveforms of signals impressed upon any segment electrode Sj to induce the display or non-display state for a matrix where n=2. Signal Sa in FIG. 8(3) is a segment drive signal when intersections D1S_(j) and D2S_(j) are both in a display state. Similarly, signal Sb in FIG. 8(4) is the corresponding signal when D1S_(j) and D2S_(j) are both in a state of non-display, signal Sc in FIG. 8(5) is the corresponding signal when D1S_(j) is in a display state and D2S_(j) in a state of non-display, and signal Sd in FIG. 8(6) is the corresponding signal when D1S_(j) is in a state of non-display and D2S_(j) is in a display state. In this case the waveforms across the electrodes of the liquid crystal are as illustrated by FIG. 7(1) and (2), and the operation margin α is √5.

FIG. 9 shows the waveform diagrams of driving signals used in three-digit matrix driving method with n=3. In FIG. 9, r₁, r₂ and r₃ represent digit drive signals, and c₀, c₁, c₃, c₁₂₃ represent segment drive signals, respectively. In FIG. 9(1), the voltage potential V_(r) of the digit drive signal is equal to the voltage potential V_(c) of the segment drive signal V_(c) and expressed as:

    V.sub.r =V.sub.c

In this case, the rms voltage V_(off) in the non-display state is √2 and rms voltage V_(on) in the display state is √6. Therefore, the operation margin α is √3.

In FIG. 9(2), V_(r) =2 V_(c), and the rms voltage V_(off) is 1 while the rms voltage V_(on) is √11/3. Therefore, the operation margin α is √11/3.

In FIG. 9(3), V_(r) =√3·V_(c), and the rms voltage V_(off) is √2(3-√3) while the rms voltage V_(on) is √2(3+√3) so that the operation margin α is ##EQU11##

FIGS. 10(1), (2) and (3) show the vector diagrams for the waveforms used in FIGS. 9(1), (2) and (3), respectively.

In FIG. 10, r₁, r₂ and r₃ indicative of varying potentials of the corresponding digit drive signals r₁, r₂ and r₃ in FIG. 9 are resolved as vectors into X, Y and Z axes, respectively. c₁, c₂, c₃, c₁₂, c₁₃ and c₂₃ correspond to voltage potentials of the segment drive signals producing display at one or two digits. From these vector diagrams, it will be possible to grasp the potential difference across the electrodes.

From the above description, it will be understood that the waveforms of the drive signals consist of a half-period (for example t₁, t₂ in FIGS. 6 and 8) and another half-period (for example t₃, t₄). Each half-period is sub-divided into n equal parts and each interval is assigned to a respective digit. Interval t₁ corresponds to a 1st digit, and interval t₂ to a 2nd digit; if the digit driving voltages are now represented with the mean value of all the digit driving signals taken as a reference, then a large driving voltage will be generated for the 1st digit driving signal over the interval t₁, the 2nd digit driving signal over the interval t₂, and the ith digit driving signal over the interval t_(i), and the voltage will drop to a low level over the other intervals. In addition, the segment signal voltage during interval t₁ and the segment signal voltage during interval t_(i) are both determined by the state of display or non-display of the 1 st digit and ith digit, respectively, in accordance with the pattern that decides which digits should be displayed by the segment signal. It is preferable that the voltage for the segment signal during the non-display state be close to the mean voltage of all the digit driving signals; even so, the rms value of the driving voltage does not fall to 0 during a state of non-display. Moreover, if we consider the driving voltage at the ith intersection when the ith digit is to be displayed, then this voltage is exactly the same as the driving voltage at the ith intersection when the ith digit is not to be displayed during the half-period from which interval t_(i) is omitted, and the rms value of the driving voltage differs only by the difference in voltage applied over the interval t_(i).

In a matrix driving method of the present invention, the driving waveform for a half cycle time is not divided in its entirety into separate components for each digit electrode and, in contrast, digit and segment drive signals are applied to digit and segment electrodes in such a manner that the digit drive signals applied to all the digit electrodes have potentials equal in level with each other during a prescribed time interval during which the potential of a first segment drive signal inducing a state of non-display at all the digit electrodes is equal to the potential of each of the digit drive signals. During the prescribed time interval, the potential difference between a second segment drive signal inducing a state of display at one of the digit electrodes and a state of non-display at the other digit electrode and each of the digit drive signals is maintained in a first predetermined value whereby the root mean square value over a complete cycle of the potential difference between the second segment drive signal and the digit drive signal applied to the other digit electrodes is substantially equal to that of the potential difference between the first segment drive signal and each of the digit drive signals. During the prescribed time interval, further, the potential difference between a third segment drive signal inducing a state of display at all the digit electrodes and each of the digit drive signals is maintained at a second predetermined value whereby the root mean square value over a complete cycle of the potential difference between the second segment drive signal and the digit drive signal applied to the said one of the digit electrodes is substantially equal to that of the potential difference between the third segment drive signal and each of the digit drive signals.

More specifically, the potential of the first segment drive signal inducing the state of non-display at all of the intersections (hereinafter referred to as display intersections) between the segment and digit electrodes has a level equal to a reference potential which is substantially equal to the mean value of all the digit drive signals. The potential of each digit drive signal in turn is selected to have a value larger than the reference potential during a respective first time interval within one-half of the cycle period. During a second time interval corresponding to the prescribed time interval mentioned above within one-half of the cycle time, the potentials of all the digit drive signals are selected to be equal to each other. The potentials of the segment drive signals inducing the state of display at only the i-th digit's display intersections and the potential of the segment drive signal inducing the state of non-display at the i-th digit's display intersections are selected to be unequal in level during the first time interval. Further, the potential of the second segment drive signal applied to a given segment electrode inducing the state of display at the display intersections of only a given digit electrode is selected to have a level by which the maximum potential difference is provided between the given digit electrode and the given segment electrode. In this case, it is possible to increase the root means square (rms) value of the driving voltage for a state of display by raising the voltage of the segment drive signal in comparison to that of the prior art, or by increasing the driving time interval in which the segment drive signal is applied, or by a combination of such methods. The third segment drive signal inducing the state of display at the display intersections of all the digit electrodes is selected to have a first potential equal to the reference potential during the first time interval and a second potential equal to the maximum value during the second time interval.

A driving method according to the present invention will now be described in general with reference to a matrix in which n=2. A voltage waveform for a digit drive signal impressed upon a digit electrode r₁ is expressed by

    Vr.sub.1 =V1+Vo,

a voltage waveform for a digit drive signal impressed upon a digit electrode r₂ is expressed by

    Vr.sub.2 =-V1+Vo,

a voltage waveform for a segment drive signal when display intersections of both digit electrode are to be brought to a state of non-display is expressed by

    VCo=Vo,

a voltage waveform for a segment drive signal indicative of a display state for both digit electrodes is expressed by

    VC.sub.12 =V2+Vo,

a voltage waveform for a segment drive signal indicative of a display state for a 1st digit electrode and non-display state for a 2nd digit electrode is expressed by

    VC.sub.1 =-2V1+Vo, and

a voltage waveform for a segment drive signal indicative of a non-display state for a 1st digit electrode and a display state for a 2nd digit electrode is expressed by

    VC.sub.2 =2V1+Vo.

Here, V1 and V2 are AC voltages which do not include a DC component;

they are chosen so as to satisfy

    ∫.sub.τ V.sub.1 ·V.sub.2 ·dt=0

    ∫.sub.τ (V.sub.2).sup.2 ·dt=8∫.sub.τ (V.sub.1.sup.2)dt

for a suitable interval τ. Vo is a function of time or a constant. By way of example, the following possibilities are acceptable: Vo=0, V1=sin ωt, and V2=√8 sin ω/2t. In such a case the rms value of the driving voltage for the display and non-display states is 3, a significant improvement over the conventional value of √5 when n=2. In order to obtain a waveform for a case in which a switchable DC power source is used for the driving operation, it is permissible to adopt a step-like voltage waveform for Vo, V1 and V₂. Two such examples are illustrated in FIGS. 11 and 14.

FIGS. 11(1) and (2) show one preferred example of the waveforms of the digit drive signals which are impressed upon respective digit electrodes r₁ ' and r₂ '. In FIG. 11(1) it can be seen that the waveform is composed of six equal time intervals t1, t2, t3, t4, t5 and t6 which constitute one cycle period. The potential levels over these time intervals (hereinafter referred to as t1, t2, t3, t4, t5 and t6) of the r₁ digit signal are t1=3 Vo, t2=2 Vo, t4=Vo, t5=2 Vo and t6=2 Vo, while the potentials for the r₂ digit signal are t1=Vo, t2=2 Vo, t3=2 Vo, t4=3 Vo, t5=2 Vo and t6=2 Vo all of these potentials being based upon the minimum potential O of the segment drive signal which is taken as a reference potential.

FIGS. 11(3), (4), (5) and (6) show the waveforms of segment drive signals C₀, C₁₂, C₁ and C₂ which are impressed upon any segment electrode Sj.

Signal Co in FIG. 11(3) is the waveform of the segment drive signal when a non-display of r₁ Sj and r₂ Sj is indicated, signal C₁₂ in FIG. 11(4) is the waveform of the segment drive signal when r₁ Sj and r₂ Sj are to be displayed, signal C₁ in FIG. 11(5) is the waveform for a display of r₁ Sj and a non-display of r₂ Sj, and signal C₂ in FIG. 11(6) is the waveform for a non-display of r₁ Sj and a display of r₂ Sj. In this example, t1 and t4 are the previously described driving intervals for all of the non-display segment signals and at the same time they also correspond to the intervals during which there is a maximum absolute value of the digit driving signal voltage with respect to the reference potential level 2 Vo. Here, the potential levels of the digit drive signals are equal to each other during intervals t2, t3, t5 and t6. In addition, two segment signals are compared and the times at which they do not present the same potential level are t1 and t4 for C₁ and C₂ and for C₀ and C₁ and for C₀ and C₂ ; all times for C₁ and C₁₂, C₂ and C₁₂. Segment signals C₁ and C₂ possess a higher absolute voltage over the respective intervals t1, t4, and although a large absolute potential difference then exists between C₁ and r₁ driving signals, a small absolute potential difference exists between C₁ and r₂ driving signals during the same interval. A large absolute potential difference also exists between C₁₂ and r₁, r₂ digit drive signals during the intervals t2 and t3.

It will now be understood that in accordance with the present invention the digit drive signals r₁ and r₂ have first and second voltage potentials 3 Vo and Vo which have the same potential difference but opposite in polarity with respect to a reference potential 2 Vo during a first time interval t1 of half cycle period H and have a voltage potential 2 Vo serving as a reference potential during a second time interval t2 or t3 of the half cycle period H, with the reference potential taking a value 2 Vo intermediate between the first and second voltage potentials 3 Vo and Vo. A first segment drive signal Co has a potential level equal to the reference potential 2 Vo during the first and second time intervals t1 and t2, inducing a state of non-display at said display elements on all of said digit electrodes. A second segment drive signal C₁ or C₂ has a fourth voltage potential 0 or 4 Vo larger in amplitude level than the first and second voltage potentials Vo and 3 Vo during the first time interval t1 and the same potential as the reference potential 2 Vo during the second time interval t2, inducing a state of display at said display elements on one of said digit electrodes. A third segment drive signal C₁₂ has the same potential as the reference potential 2 Vo during the first time interval t₁ and a voltage potential 4 Vo, during the second and third time intervals t2 and t3, inducing a state of display at said display elements on all of said digit electrodes.

FIG. 12 shows the waveforms for the potential difference across the electrodes. FIGS. 12(1), (2), (3), (4), (5) and (6) are the respective waveforms for the intersections r₁ ×C₁₂, r₂ ×C₁₂, r₁ ×C₀, r₂ ×C₀, r₁ ×C₁, and r₂ ×C₁. If a square wave with a peak value of √8 Vo is employed as the C₁₂ waveform it is possible to do away with the intervals t2, t3, t5, t6, and 3 can still be obtained as the ratio of the rms value of the display to the non-display driving voltage.

FIG. 13 shows the vector diagrams illustrating the relationship between the digit and segment drive signals used in FIG. 11. In FIG. 13, the potential C₀, having a value of 2 V, of the segment drive signal C₀ ' is plotted as a vector at the origin 0 and the potentials 3 V and 4 V are illustrated as having values 1 and 2, respectively, for a sake of simplicity of description. In FIG. 13(1), the potentials r₁ and r₂ of digit drive signals r₁ and r₂ are plotted on the Y axis and symmetrical with respect to the potential C₀ of the segment drive signal C₀ plotted on the intersection between the X and Y axes. Assume that r₁ r₂ =2 R. In this case, r₁ is plotted as a vector on the point (O,R) indicative of the potential, and r₂ is plotted as a vector on the point (O,-R) indicative of the potential. Plotting C₂ as a vector on the point (O,2 R) and C₁ on the point (O,- 2 R), then the following relation holds: ##EQU12## Here, the potential differences between r₁ and C₁₂ and between r₂ and C₁₂, represented by r₁ C₁₂ and r₂ C₁₂, are equal to each other when C₁₂ falls on the X axis and the distance between the points C₀ and C₁₂ is √8 R. Therefore, the absolute value of the vector a is equal to R and the absolute value of the vector b is equal to 3 R. From this it will be seen that the operation margin is 3 which is much greater than that obtained in the prior art driving method.

In the vector diagram of FIG. 13(1), since C₀ is set to the reference potential 0 to which G is also set, the potential of each point at a certain time instant in interval t₁ is expressed as:

C₁ =-2

r₂ =-1

C₁₂ =0

r₁ =1

C₂ =2

From the above equations it will be seen that it is possible practically to obtain driving waveforms with the use of four voltage sources and varying in potential at five different levels.

FIG. 13(2) shows the vector diagram defined in the three dimensions using X, Y and Z axes. In this vector diagram, the time interval t₁ is assigned to the X axis, t₂ to the Y axis and t₃ to the Z axis. The potentials of various drive signals are expressed by the following matrix: ##EQU13## The above relation represents the potentials at the time intervals t₁, t₂ and t₃ which constitutes one-half of cycle time of the drive signals. The potentials in another half cycle time will be obtained by multiplying the value of -1 to each of the potentials listed above. It is to be noted that the difference between the potential of the segment drive signal inducing a state of display at one of the digit electrodes and the mean value of all the digit signals is preferably selected to have a value two times the difference between the mean value of the potentials of all the digit drive signals and the potential of the digit drive signal applied to the digit electrode which is to be in a state of display.

FIGS. 14(1) and (2) shows another preferred example of the waveforms of digit drive signals which are impressed upon respective digit electrodes r₁ ' and r₂ '. In FIG. 14(1) it can be seen that the waveform is composed of four equal time intervals t1, t2, t3 and t4 which constitute one cycle period. The potential levels over the 1st half cycle time and 2nd half cycle period (hereinafter referred to as t1, t2, t3, and t4) of the r₁ digit signal are t1=3 Vo, t2=2 Vo, t3=Vo and t4=2 Vo, while the potentials for the r₂ digit signal are t1=Vo, t2=2 Vo, t3=3 Vo and t4=2 Vo, all of these potentials being based upon the minimum potential of the segment driving signal which is taken as a standard.

FIGS. 14(3), (4), (5) and (6) show the waveforms of the segment drive signals which are impressed upon any segment electrode Sj.

Signal C₀ in FIG. 14(3) is the waveform of the segment electrode driving signal when a non-display of r₁ Sj and r₂ Sj is indicated, signal C₁₂ in FIG. 14(4) is the waveform of the segment electrode driving signal when r₁ Sj and r₂ Sj are to be displayed, signal C₁ in FIG. 14(5) is the waveform for a display of r₁ Sj and a non-display of r₂ Sj, and signal C₂ in FIG. 14(6) is the waveform for a non-display of r₁ Sj and a display of r₂ Sj. In this example, t1 and t3 are the previously described driving intervals for all of the non-display segment signals and at the same time they also correspond to the intervals during which there is an increase in the absolute value of the digit driving signal voltage with respect to the reference potential level 2 Vo. Here, the potential levels of the two digit drive signals are equal to each other during intervals t2 and t4. In addition, two segment signals are compared and the times at which they do not present the same potential level are t₁ and t₃ for c₀ and c₁, c₀ and c₂, t₁ ", t₂ and t₃ " for c₁ and c₁₂, t₁ ', t₂ and t₃ ' for c₂ and c₁₂. Segment signals c₁ and c₂ possess a higher absolute voltage of over the intervals t₁, t₃ than is the case with the prior art, and although a large driving voltage is generated between c₁ and the r₁ driving signal, a small driving voltage generated between c₁ and r₂ driving signal over the same interval will suffice. A large driving voltage is also generated between c₁₂ and the r₁, r₂ digit driving signals over the intervals t₂ , t₄ as well as t₁, t₃. It is to be understood that FIGS. 11 and 14 show examples in which the potential of the segment drive signal inducing the state of non-display at display intersections of all the digit electrodes is equal to the mean value of the potentials of all the digit drive signals, i.e., the vector C₀ is brought into coincidence with the vector G and the vectors C₁, r₁ and G are disposed on the same axis.

In FIG. 14, more specifically, the first digit drive signal r₁ has a first voltage potential 3 V_(O) during a first time interval t₁ of a first half cycle period H₁ and a reference potential 2 V_(O) during a second or remaining time interval t₂ of the first half cycle period H₁. The second digit drive signal r₂ has a second voltage potential V_(O) which is opposite in polarity to the voltage potential 3 V_(O) of the first digit drive signal r₁ during the first time interval t₁. During a first time interval t₃ of another half cycle period H₂ the first digit drive signal r₁ has a voltage potential V_(O), and the second digit drive signal r₂ has a voltage potential 3 V_(O), which provides the same voltage difference as that between 2 V_(O) and V_(O) and is opposite in polarity to the voltage potential V_(O) of the first digit drive signal r.sub. 1 with respect to the reference potential 2 V_(O). During the second time interval t₄ of another half cycle period H₂, the first and second digit drive signals r₁ and r₂ have the reference potential 2 V_(O). A segment drive signal C₀ has a voltage potential equal to the reference potential 2 V_(O) during the first and second time intervals t₁ and t₂ of the first half cycle period H₁ and during the first and second time intervals t₃ and t₄ of another half cycle period H₂, inducing a state of non-display at display elements on all of the digit electrodes because of a minimum potential difference between the digit electrodes and the segment electrodes as seen in FIGS. 15(3) and (4). A segment signal C₁₂ has a voltage potential 0 during a time period t₁, of the first time interval t₁ of the half cycle period H₁ and a voltage potential 4 V_(O) during another time period t₁ of the first time interval t₁. During the second time interval t₂ of the first half cycle period H₁ the segment drive signal C₁₂ has the voltage potential 4 V_(O), so that the maximum potential difference exists between the digit and segment electrodes as shown in FIGS. 15(1) and (2), inducing a state of display at display elements on all the digit electrodes. The segment drive signal C₁ has a voltage potential 0 during the first time interval t.sub. 1 of the first half cycle period H₁, a voltage potential 2 V_(O) during the second time interval t₂ of the first half cycle period H₁, a voltage potential 4 V_(O) during the first time interval t₃ of the second half cycle period H₂, and a voltage potential 2 V_(O) during the second time interval t₄ of the second half cycle period H₂. Thus, the maximum potential difference exists between the segment drive signal c₁ and the digit drive signal r₁, inducing a state of display at display elements on the first digit electrode applied with digit drive signal r₁. The segment drive signal c₂ has a voltage potential 4 V_(O) during the first time interval t₁ of the first half cycle period H₁, a voltage potential 2 V_(O) during the second time interval t₂ of the first half cycle period H₁, a voltage potential 0 during the first time interval t₃ of the second half cycle period H₂, and a voltage potential 2 V_(O) during the second time interval H₂ of the second half cycle period H₂. Thus, the maximum potential difference exists between the segment drive signal C₂ and the digit drive signal r₂, inducing the state of display at the display elements on the digit electrode applied with digit drive signal r₂. It will thus be seen that during the second time intervals t₂ and t₄ of the first and second half cycle periods H₁ and H₂ the segment drive signals c₁ and c₂ have the voltage potential equal to the reference voltage potential, but during the first time intervals t₁ and t₃ of the half cycle periods the segment drive signals c₁ and c₂ have the voltage potential 0 or 4 V_(O).

FIGS. 15(1), (2), (3), (4), (5) and (6) are the respective waveforms for the intersections c₁₂ ×r₁, c₁₂ ×r₂, c₀ ×r₂, c₀ ×r₁, c₂ ×r₁, c₂ ×r₂. If a square wave with a peak value of √8 Vo is employed as the c₁₂ waveform, it is possible to do away with the intervals t₂, t₄, and 3 can still be obtained as the ratio of the root mean square value of the display to the non-display driving voltage.

FIG. 16 shows another example of the waveform diagram for drive signals. In the example of FIG. 16, each of the digit drive signals r₁ and r₂ have a reference voltage potential 2 V_(O) during a first half cycle H₁ of a cycle period and a reference voltage potential V_(O) during a second half cycle time H₂. During a first time interval t₁ of the first half cycle time H₁, the first digit drive signal r₁ has a voltage potential 3 V_(O) and the second digit drive signal r₂ has a voltage potential V_(O) which provides the same voltage difference as that between the potential 3 V_(O) of the first digit drive signal r₁ and the reference potential 2 V_(O) during the first time interval t₁. During the second time interval t₂ of the first half cycle time H₁, both the first and second digit drive signals r₁ and r₂ have the voltage potential equal to the reference voltage potential 2 V_(O). During a third time interval t₃ of the first half cycle time H₁, the first digit drive signal r₁ has a voltage potential v_(O) and the second digit drive signal r₂ has a voltage potential 3 V_(O) of the same potential difference as that of the first digit drive signal r₁ relative to the reference potential 2 V_(O) but opposite in polarity with respect to the reference potential 2 V_(O). As previously noted, the reference voltage potential of the first and second digit drive signals r₁ and r₂ is V_(O) during the second half cycle time H₂. During a first time interval t₄ of the second half cycle time H₂, the first digit drive signal r₁ has a voltage potential 0 and the second digit drive signal r₂ has a voltage 2 V_(O) of the same potential difference as that of the first digit drive signal r₁ but opposite in polarity to the first digit drive signal r₁ with respect to the reference potential V_(O). During a second time interval t₅ of the second half cycle time H₂, the first and second digit drive signals r₁ and r₂ have a voltage potential equal to the reference potential V_(O). During a third time interval t₆ of the second half cycle time H₂, the first digit drive signal r₁ has a voltage potential 2 V_(O) and the second digit drive signal r₂ has a voltage potential 0 of the same potential difference as that of the first digit drive signal r₁ but opposite in polarity thereto with respect to the reference potential V₀.

In FIG. 16, a segment drive signal C₀ has a voltage potential equal to the reference potential 2 V_(O) of the digit drive signals during the first half cycle time H₁ and has a voltage potential equal to the reference potential V_(O) of the digit drive signals during the second half cycle time H₂, providing a minimum voltage difference between the digit drive signal and the segment drive signal C₀, as shown in FIG. 18(1), to induce a state of non-display at display elements on all of the digit electrodes. A segment drive signal C₁₂ has a voltage potential 0 during the first half cycle time H₁ and has a voltage potential 3 V_(O) during the second half cycle time H₂, providing a maximum voltage difference between the segment drive signal C₁₂ and either one of the first and second digit drive signals r₁ and r₂, as shown in FIG. 18(2) to induce a state of display at all the display elements on both the first and second digit electrodes. A third segment drive signal C₁ has a voltage potential 0 during the first time interval t₁ of the first half cycle time H₁ and a voltage potential 3 V_(O) during the second and third time intervals t₂ and t₃ of the first half cycle time H₁. The segment drive signal C₁ has a voltage potential 3 V_(O) during the first time interval t₄ of the second half cycle time H₂ and a voltage potential 0 during the second and third time intervals t₅ and t₆ of the second half cycle time H₂, providing a maximum voltage difference between the first digit drive signal and the segment drive signal C₁ and a minimum voltage difference between the digit drive signal r₂ and the segment drive signal c₂ as shown in FIG. 18(3). In this case, the display elements associated with the first digit electrode applied with the first digit drive signal r₁ are turned on while the display elements associated with the second digit electrode applied with the second digit drive signal r₂ are turned off. Similarly, a segment drive signal c₂ has a voltage potential 3 V_(O) during the first and second time intervals t₁ and t₂ of the first half cycle time H₁ and a voltage potential 0 during the third time interval t₃ of the first half cycle time H₁. The segment drive signal c₂ also has a voltage potential 0 during the first and second time intervals t₄ and t₅ of the second half cycle time and a voltage potential 3 V_(O) during the third time interval t₆ of the second half cycle time H₂. Thus, a maximum voltage difference is provided between the segment drive signal c₂ and the digit drive signal r₂ while a minimum voltage difference is provided between the segment drive signal c₂ and the digit drive signal r₁, as shown in FIG. 18(3). In this instance, the display elements associated with the digit electrode applied with the digit drive signal r₂ are turned on while the display elements associated with the digit electrode applied with the digit drive signal r₁ are turned off.

FIGS. 16(1) and (2) show digit driving waveforms which are applied to respective digit electrodes r₁ ' and r₂ '. In FIG. 16(1) it can be seen that the waveform is composed of 6 equal time intervals t₁, t₂, t₃, t₄, t₅, and t₆ which constitute one period. The potential levels over the 1st half cycle time H₁ and 2nd half cycle time H₂ (hereinafter referred to as t₁, t₂, . . . t₆) of the r₁ digit signal are t₁ =3 Vo, t₂ =2 Vo, t₃ =Vo, t₄ =0, t₅ =Vo, and t₆ =2 Vo, while the potentials for the D2 digit signal are t₁ =Vo, t₂ =2 Vo, t₃ =3 Vo, t₄ =2 Vo, t₅ =Vo, and t₆ =0, all of these potentials being based upon Vo which is taken as a reference potential. If the potentials over each of the intervals t₁, t₂. . . for the r₁ digit signal and r₂ digit signal are added, we are left with t₁ =4 Vo, t₂ =4 Vo, t₃ =4 Vo, t₄ 2 Vo, t₅ 2 Vo, and t₆ = 2 Vo. If a comparison is made to the waveforms shown in FIG. 8, it will be seen that in FIG. 16 intervals t₂ and t₅ have been added; in other words, intervals have been added over which the potentials of the r₁ and r₂ digit signals coincide.

FIG. 16(3), (4), (5) and (6) show the waveforms which are impressed upon any segment electrode Sj. Signal Co in FIG. 16(3) is the waveform of the segment electrode driving signal when a non-display of r₁ Sj and r₂ Sj is indicated, signal c₁₂ in FIG. 16(4) is the waveform of the segment electrode driving signal when r₁ Sj and r₂ Sj are to be displayed, signal c₁ ' in FIG. 16(5) is the waveform for a display of r₁ Sj and a non-display of r₂ Sj, and signal c₂ ' in FIG. 16(6) is the waveform for a non-display of r₁ Sj and a display of r₂ Sj. The segment electrode driving signals which satisfy all states are a combination of the potentials (Vo·2 Vo) and (0·3 Vo), and their frequency is the same as the frequency of the digit driving signals.

FIG. 17 show the vector diagram for the drive signals shown in FIG. 16. Here, the potentials of the various drive signals are expressed by the following matrix: ##EQU14## In this case, the vectors a and b are written as: ##EQU15## Therefore, the operation margin α is obtainerd as:

    α=√7

In this example, the varying potential C₀ of the segment drive signal C₀ ' is plotted as a vector at a point intermediate between potentials r₁ and r₂ and coincides with G; Angle C₁ Gr₁ and C₂ Gr₂ define obtuse angles. This means that the potential of the segment drive signal inducing a state of non-display at all the digit electrodes is equal to the mean value of the potentials of all the digit drive signals.

It can thus be understood that the driving method of the present invention, in contrast to that of the prior art, is provided with intervals over which there is coincidence between the phases of the digit electrode driving signals as well as coincidence between their potentials. In this case, if a non-display is indicated for segments at matrix intersections, the segment electrodes may be applied with a voltage at the same level as the digit signal potentials when these potentials are in coincidence, whereas they are applied with differing voltage levels at other times. It should be appreciated that in the examples of FIGS. 11 and 14 the digit and segment drive signals have five potential levels different from each other by equal steps and in the example of FIG. 16 the digit and segment drive signals have four potential levels differing from each other by equal steps.

FIG. 18 shows the waveforms which appear across the electrodes in a case where the waveforms of FIG. 17 are applied to a liquid crystal. FIG. 18(1) shows examples of potential waveforms between digit and segment electrodes when a state of non-display is desired at all of the digit electrodes, and FIG. 18(2) examples in which a display is desired at all of the digit electrodes. FIG. 18(3) shows an example in which a display is desired at the first digit electrodes and a state of non-display is desired at the second digit electrode.

In FIG. 18(2) the rms voltage is √14/3 Vo, while the rms voltage is √2/3 Vo according to FIG. 18(1), thereby giving an operation margin of α=√7. In other words, the operation margin can be widened from √5 to √7 by providing an interval over which the potential levels of the two digit driving signals of FIG. 17 coincide.

FIG. 19A shows the waveform diagram of other example of driving signals used in the method of the present invention with n=3. In the waveform diagram of FIG. 19A, a digit drive signal r₂ has a reference voltage potential 2 V_(O) and digit drive signals r₁ and r₃ have voltage potentials 3 V_(O) and V_(O), respectively, during a first time interval t₁ of a half cycle period, with the voltage potentials 3 V_(O) and V_(O) being of the same amplitude level relative to the reference voltage potential 2 V_(O) but opposite in polarity to one another with respect to the reference voltage potential 2 V_(O). During a second time interval t₂ of the half cycle period, the digit drive signal r₃ has a voltage potential equal to the reference potential 2 V_(O) and the digit drive signals r₁ and r₂ have voltage potentials V_(O) and 3 V_(O), respectively, which have the same potential difference relative to the reference potential 2 V_(O) and are opposite in polarity to one another with respect to the reference potential 2 V_(O). During a third time interval of the half cycle period, the digit drive signal r₁ has the reference potential and the digit drive signals r₂ and r₃ have the voltage potentials V_(O) and 3 V_(O), respectively, which have the same potential difference relative to the reference potential 2 V_(O) but are opposite in polarity to one another with respect to the reference potential 2 V_(O). During fourth to six time intervals t₄ to t₆, all of the digit drive signals r₁ to r₃ have the reference potential 2 V_(O).

In FIG. 19A, a segment drive signal c₀ has a voltage potential equal to the reference potential 2 V_(O) during all of the time intervals t₁ through t₆ of the half cycle period, providing a minimum voltage difference between the segment drive signal c₀ and any one of the digit drive signals r₁ and r₂ to induce a state of non-display at all the display elements associated with the digit electrodes applied with the digit drive signals r₁ through r₃. A segment drive signal c₁ has such a voltage potential to provide a maximum voltage difference between the segment drive signal c₁ and the digit drive signal r₁ to induce a state of display at the display elements associated with only the digit electrode applied with the digit drive signal r₁. More specifically, the segment drive signal c₁ has a voltage potential V_(O) during the first time interval t₁ and a voltage potential 3 V_(O) during the second time interval t₂. During the remaining time intervals t₃ through t₆, the segment drive signal c₁ has a reference voltage 2 V_(O). Thus, a maximum voltage difference is provided between the first digit drive signal r₁ and the segment drive signal c₁ during the first and second time intervals t₁ and t₂ as shown in FIG. 20 so that the display elements associated with the digit electrode applied with the digit drive signal r₁ are turned on during the first and second time intervals t₁ and t₂. During the remaining time intervals t₃ through t₆, a minimum voltage difference is provided between the segment drive signal c₁ and the digit drive signal r₁ so that the display elements associated with the digit electrode applied with the digit drive signal r₁ are turned off during the time intervals t₃ through t₆. A voltage difference between the digit drive signal r₂ and the segment drive signal c₁ exists as shown in the waveform r₂ -c₁ of FIG. 20 and the display elements are turned off. Likewise, a voltage difference exists between the digit drive signal r₃ and the segment drive signal c₁ as shown by the waveform r₃ -c₁ of FIG. 20 and the display elements are turned off. A segment drive signal c₂ has voltage potentials of such a value to provide a maximum voltage difference between the segment drive signal c₂ and the digit drive signal r₂ during the time intervals t₂ and t₃ of the half cycle period.

FIGS. 19A(4), (5), (6), (7), (8), (9), (10) and (11) show the waveforms which are impressed upon any segment electrode Sj. Signal Co in FIG. 19A(4) is the waveform of the segment electrode driving signal when a non-display of r₁ Sj, r₂ Sj and r₃ Sj is indicated, signal c₁₂ in FIG. 19A(8) is the waveform of the segment electrode driving signal when r₁ sj and r₂ Sj are to be displayed and r₃ Sj is to be non-displayed, signal c₁ in FIG. 19A(5) is the waveform for a display of r₁ Sj and a non-display of r₂ Sj and r₃ Sj, and signal c₂ in FIG. 19A(6) is the waveform for a non-display of r₁ Sj and r₃ Sj and a display of r₂ Sj.

Similarly, signal C₃ in FIG. 19A(7) is the waveform for a display of r₃ Sj and a non-display of r₁ Sj and r₂ Sj, signal C₁₃ in FIG. 19A(9) is the waveform for a display of r₁ Sj and r₃ Sj and a non-display of r₂ Sj, signal C₂₃ in FIG. 19A(10) is the waveform for a display of r₂ Sj and r₃ Sj and a non-display of r₁ Sj, and signal C₁₂₃ in FIG. 19A(11) is the waveform for a display of r₁ Sj, r₂ Sj and r₃ Sj.

It is to be appreciated that in the example of FIG. 19A, the difference between the potential of the segment drive signal inducing a state of display at one of the digit electrodes and the potential of the mean value of all the digit drive signals is equal to the potential difference between the mean value of the potentials of all the digit drive signals and the potential of the digit drive signal applied to the digit electrode which is to be in a state of display. It should also be appreciated that the digit drive signals r₁, r₂ and r₃ have first, second and third potential levels Vo, 2 Vo and 3 Vo, respectively, and that the three digit drive signals concurrently have the different potential levels during the time intervals t₁, t₂ and t₃ and have the same potential level during the time intervals t₄, t₅ and t₆.

FIG. 19B shows a model matrix layout for the digit and segment drive signals shown in FIG. 19A, wherein the three digit electrodes are employed.

FIG. 20 shows an example of the waveforms for the potential difference across the digit and segment electrodes with the drive signals used in FIG. 19A.

FIG. 21(1) shows the vector diagram for the drive signals shown in FIG. 19A. In FIG. 21(1), a varying potential C₀ of the segment drive signal C₀ ' indicative of the non-display state of all the digit electrodes r₁ ', r₂ ' and r₃ ' is plotted as a vector at a potential intermediate among potentials r₁, r₂ and r₃ of the digit drive signals r₁ ', r₂ ' and r₃ '. Let C₀ r₁ =C₀ r₂ =C₀ r₃ =R. r₁ r₂ r₃ define an equilateral triangle about C₀ as a center with the line segment having the length of √3·R. In this case, C₁ C₂ C₃ are expressed as: ##EQU16## Therefore, r₁ C₃ r₂ C₁ r₃ C₂ define an equilateral hexagon about C₀ as a center. Each point of C₁₂, C₁₃, C₂₃, C₁₂₃ are selected such that r₁ C₂₃ =R and r₂ C₂₃ =r₃ C₂₃. The point of C₁₂₃ is selected such that r₁ C₁₂₃ =r₂ C₁₂₃ =r₃ C₁₂₃. The vectors a and b are expressed as:

    |a|=R

    |b|=2R

Therefore, the operation margin α is obtained as:

    α=2

FIG. 21(2) shows an example of the diagram in which the arrangement of FIG. 21(1) is applied to the points of a three-dimentional lattice. In FIG. 21(2) potentials C₁₂, C₁₃, C₂₃ and C₁₂₃ of the corresponding segment drive signals C₁₂ ', C₁₃ ', C₂₃ ' and C₁₂₃ ' can be represented as vectors at points within three-dimensional space; however, by doing so the points indicative of potentials will no longer rest at the points of a regular lattice. In order to permit the potential indicating points to lie at the points of a regular lattice, at least 4-dimensions are required. Therefore, the potentials r₁, r₂, r₃, C₀, C₁, C₂ and C₃ are plotted as vectors on the X, Y and Z axes. FIG. 21(3) shows an example of the diagram in which C₁₂, C₁₃, C₂₃ and C₁₂₃ lie on the regular lattice defined by the X', Y' and Z' axes with the potentials r₁, r₂, r₃, C₀, C₁, C₂ and C₃ being at the origin of the X', Y' and Z' axes. If the matrix is used to show this, the following is the result: ##EQU17## From the above it will be seen that the half frame time consists of six equal time intervals t₁ through t₆. The potentials for the remaining frame time can be obtained by multiplying each element of the above matrix by -1. It should now be understood that in FIG. 21(2) the potentials C₀, C₁, C₂ and C₃ are plotted in terms of the time t₁, t₂ and t₃ assigned to the X, Y and Z axes whereas in FIG. 21(3) the potentials C₁₂, C₁₃, C₂₃ and C₁₂₃ are plotted in terms of the times t₄, t₅ and t₆ assigned to the X', Y' and Z' axes.

It will now be appreciated that the waveforms of the matrix drive signals can be represented in vector space as previously noted. The set of digit drive signals capable of displaying a complete pattern is given by:

    1/T∫.sup.τ r.sub.i.sup.2 dt=R.sup.2

    1/T∫.sup.τ r.sub.i r.sub.j dt=-R.sup.2 /n-1

Therefore, the digit drive signal is located on the surface of a sphere of radius R with the origin as a center. It can be understood from ##EQU18## that the distance between mutual drive signals is given by √2n/n-1R. For a two-digit matrix, r₁ and r₂ become points of symmetry with respect to the origin. For a three-digit matrix, r₁, r₂, r₃ define an equilateral triangle with a side of √3 R. For a four-digit matrix, the points lie at the corners of an equilateral tetrahedron. In the case of an n-digit matrix, the points lie at the apices of an equilateral n(n-1)(n-2)/6 body in the n-1 dimension space. It can be understood that the digit drive signals of the prior art satisfy these conditions. Hereinafter such digit drive signals will be referred to as digit drive signals which possess symmetry.

The segment drive signal Cm which displays the worst pattern is given by: ##EQU19##

Where Σ is the sum total with regard to digit electrodes which are to be in the state of display. Therefore, the segment drive signal Cm can readily be obtained from the position of the centroid Σr_(i) /m of the digit drive signal for the digit electrode which is to be in the state of display. It can be understood that the varying potential difference between the potential of the segment drive signal inducing a state of display at one of the digit electrodes and the mean value of the potentials of all the digit electrodes is in a proportional relationship with the varying potential difference between the mean value of the potential of all the digit drive signals and the potential of the digit drive signal applied to the digit electrode which is to be in a state of display.

FIG. 22 shows the waveforms for another example of drive signals in accordance with the present invention. Here n=3 and three potential levels are employed. FIGS. 22(1), (2) and (3) depict the digit drive signal waveforms which are impressed upon respective digit electrodes r₁ ', r₂ ' and r₃ '. FIGS. 22(4) through (11) show segment drive signals Co' through C₁₂₃ ' which correspond to the combined patterns for the display and non-display of digits. t1, t2, . . . t8 denote one-eighth divisions of a signal period (frame time) T. t1', t2', t3' and t4' denote subintervals within the respective intervals t1, t2, t3 and t4; t1', t2' and t3' represent a value of T/16, a t4' a value of T/32. For the sake of convenience the voltages over the intervals t5, t6, t7, and t8 are taken to be the reverse in polarity of those over t1, t2, t3 and t4 with respect to the reference line Vo. FIG. 22(4) shows the voltage waveform of a segment signal Co' indicative of a non-display for all digits, FIGS. 22(5), (6) and (7) depict the voltage waveforms of segment signals C₁ ', C₂ ' and C₃ ' indicative of a state of display for only one digit of respective digits r₁ ', r₂ ' and r₃ '. FIGS. 22(8), (9) and (10) depict the voltage waveforms for segment signals C₂₃ ', C₁₃ ' and C₁₂ ' indicative of a state of non-display for one digit of respective digits r₁ ', r₂ ' and r₃ ', and FIG. 22(11) shows the voltage waveform for a segment signal C₁₂₃ ' indicative of a state of display for all digits. According to the prior art, when n=3 and d=1, √3 is the ratio of the root mean square value for the driving voltage of the display state to the non-display state; according to the present invention, the ratio is 2 by which the display contrast is remarkably improved.

It will now be appreciated from FIGS. 13, 17 and 21 that in vector diagram each of angles C₀ r₁ G, C₀ r₂ G, . . . and C₀ r_(n) G is less than 45 degrees in which C₀ is the vector indicative of a varying potential of the segment drive signal applied to the segment electrode inducing a non-display state at all of the digit electrodes, r₁, r₂, . . . and r_(n) are the vectors of varying potentials of the digit drive signals, and G is the potential indicating vector represented by the mean value of the potentials of all the digit drive signal and in which C₀ is substantially coincident with G; each of angles C₁ Gr₁, C₂ Gr₂, . . . and C_(n) Gr_(n) defines an obtuse angle in which C₁, C₂, . . . and C_(n) are the vectors of the segment drive signals applied to the segment electrodes inducing a display state at a corresponding one of the digit electrodes alone; and the line segments C₁ C₀, C₂ C₀, . . . and C_(n) C₀ tying the vectors C₁, C₂, . . . and C_(n) and the vector C₀ define between each pair an obtuse angle. When the number of digit electrodes is 2, further, the cosine of the angle C₀ r₁ G is greater than √1/2 and the cosine of each of the angles C₁ r₁ G, C₂ r₂ G . . . is greater than

    A/(1+√2)+1/2A

in which A is the cosine of the angle C₀ r₁ G. When the number of digit electrodes is 3, further more, the cosine of the angle C₀ r₁ G is greater than 2/3 and the cosine of each of the angles C₁ r₁ G, C₂ r₂ G and C₃ r₃ G is greater than

    (√3-1)A/√2+√2/3A

in which A is the cosine of the angle C₀ r₁ G.

In summary, the operation margin can be increased in a driving method of the present invention by (1) selecting the potential of the segment drive signal C₀ inducing the state of non-display at all of the digit electrodes to be approximately equal to the mean value G of the potentials of all of the digit drive signals while maintaining the relationship

    C.sub.0 r.sub.1 ≈C.sub.0 r.sub.2 ≈. . .

and by (2) selecting the potentials C₁, C₂ . . . of the segment drive signals such that C₁ r₁ G approximately defines a straight line on the vector diagram and the line segments defined by C₁ r₂, C₁ r₃ . . . are substantially equal to the line segment defined by C₀ r₁ in the vector diagram.

In the prior art matrix driving method, since the potential of the segment drive signal is selected to a value such that the vectors of the segment drive signals are located on the apices of a cube in an n-dimension space, each of angles C₁ C₀ C₂, C₁ C₀ C₃, C₂ C₀ C₃ . . . defines a right angle. Therefore, the conditions (1) and (2) mentioned above can not be satisfied by the prior art matrix driving method. In the matrix driving method of the present invention, on the contrary, the potentials C₀, C₁, C₂ . . . of the segment drive signals are selected to have values such that each of the angles C₁ C₀ C₂, C₁ C₀ C₃, C₂ C₀ C₃ . . . is an obtuse angle whereby the above noted conditions (1) and (2) can be satisfied.

Next, the potential of each of the segment drive signals C₁₂ inducing the state of display at two of the digit electrodes . . . is selected to have a value which satisfies the following relation: ##EQU20## In a modified example, i.e., in a case in which it is difficult to provide a larger potential difference between the segment drive signal C₁₂ ' inducing the state of display at all the digit electrodes and each of the digit drive signals r₁ ', r₂ ' . . . , the potential of the segment drive signal C₀ ' and the potentials of the digit drive signals r₁ ', r₂ ' . . . are selected to have the same level during a predetermined time interval during which the potential difference exists between the segment drive signal C₁₂ ' and each of the digit drive signals r₁ ', r₂ ' . . . in such a manner as shown in FIG. 16.

The above noted conditions (1) and (2) can be more clearly explained by the geometrical analysis. Let the cosine of angle C₀ r₁ G be A and the cosine of angle C₁ r₁ G be B, the operation margin α is expressed as: ##EQU21## in which x and y denote the factors of A and are written as:

when n=2, x=2A and y=1

when n=3, x=3A/2 and y=√1-3A² /4 With n=2, let A>√1/2 and ##EQU22## In this case, the maximum operation margin α obtained in the prior art driving method is expressed by:

    α=√2+1

With n=3, let A>√2/3 and ##EQU23## In this case, the maximum operation margin α obtained in the prior art driving method is expressed by: ##EQU24## It is to be noted that the operational margin can be increased to the maximum value by letting A=B=1. This example is shown in FIG. 11, 14, 19 and 22 in which the operation magin is 3 when n=2, and 2 when n=3.

FIG. 23 illustrates a block diagram of electric circuitry of a drive system for an electro-optical display device including digit and segment electrodes arranged in a matrix configuration. The drive system shown in FIG. 23 is arranged to produce drive signals having the waveforms as shown in FIG. 11 by way of example. The drive system has a power source 50 such as a battery to provide outputs at 0 volts and V volts. A D.C. converter 52 is connected to the power source 50 to provide output voltages at 0, V, 2 V, 3 V and 4 V. The power source 50 also connected to an oscillator circuit 54 operating at a relatively high frequency. This relatively high frequency is supplied to a frequency converter 56 in the form of a divider which divides down the frequency from the oscillator circuit 54 to provide low frequency signals. These low frequency signals are applied to the D.C. converter 52, a timing pulse generator 58 and a logic circuit 60. The timing pulse generator 58 generates various timing signals at predetermined frequencies in response to the low frequency signals from the frequency converter 56. These timing signals are applied to a digit driver 62 and a segment signal generator 64. The digit driver 62 generates digit drive signals r₁ ' and r₂ ' having waveforms shown in FIG. 11 in response to the timing signals delivered from the timing pulse generator 58 and the voltage signals V, 2 V and 3 V delivered from the D.C. converter 52. The digit drive signals are applied to digit electrodes of an electro-optical display device 65 which may be a liquid crystal. The segment signal generator 64 generates segment signals C₀ ', C₁ ', C₂ ' and C₁₂ ' having the waveforms shown in FIG. 11 in response to the timing signals from the timing signal generator 64 and output voltages 0, 2 V and 4 V delivered from the D.C. converter 52.

The logic circuit 60 generates outputs in response to the low frequency signal delivered from the frequency converter 56. These outputs are applied to a decoder 66, which generates decoded outputs. The decoded outputs are applied to a segment driver 68, to which the segment drive signals are also applied. The segment driver 68 delivers selected one of the segment drive signals to selected one of segment electrodes arranged in a matrix configuration with respect to the digit electrodes. In this manner, the display device 65 effects a display or non-display at desired segments or display elements in a particular pattern in dependence on the digit drive signal and the segment drive signal applied to the display device.

FIG. 24 shows a detailed circuit connection for the digit electrodes and the segment electrodes of a portion of the display device 65 shown in FIG. 23. s shown in FIG. 24, each digit includes four segment electrodes such as Wa, Wb, Wc and Wd and each segment electrode has first and second portions disposed opposite the first and second digit electrodes r₁ ' and r₂ ', respectively.

FIG. 25 shows an example of the timing signal generator 58 shown in FIG. 23. As shown, the timing signal generator 58 comprises a level shifter 70 which generates a clock signal φ₂ having the potential 4 V as shown in FIG. 26 in response to a clock signal φ₁ from the frequency converter and output voltages 0 and 4 V delivered from the D.C. converter 52 (see FIG. 23). The clock signal φ₂ is applied to a count-by-6 ring counter 72 composed of a plurality of flip-flop P₁ through P₆. The flip-flop P₁ and P₄ generate timing signals A₁ and A₃ as shown in FIG. 25. The outputs of the flip-flops P₂ and P₃ are connected to an OR gate 74, which generates a timing signal A₂. Likewise, the outputs of the flip-flops P₅ and P₆ are connected to an OR gate 76, which generates a timing signal A₄. The waveforms of the timing signals A₂ and A₄ are shown in FIG. 26.

FIG. 27 shows an example of the segment signal generator 64 shown in FIG. 23. The segment signal generator 64 comprises a plurality of input terminals 80, 82, 84 and 86, and a plurality of switching circuits 88, 89 and 90 having their outputs connected to terminals 92, 94 and 96 labelled C₁₂ ', C₁ ' and C₂, respectively. The switching circuit 88 is composed of transmission gates TG1 through TG4 having control gates connected to the input terminals 80, 82, 84 and 86 to receive the timing signals A₁, A₂, A₃ and A₄, respectively. The transmission gates TG1 through TG4 also have inputs connected to terminals 102, 100, 102 and 104 to receive the output voltages 2 V, 4 V, 2 V and 0 delivered from the D.C. converter 52, respectively. Outputs of the transmission gates TG1 through TG4 are coupled together and connected to the outputs terminals 92. With this arrangement, when the timing signal A₁ goes to a high logic level during the time interval t₁ as shown in FIG. 26, the transmission gate TG1 is turned on, and the output terminal 92 is connected to the terminal 102. Therefore, the segment drive signal C₁₂ ' has the potential of 2 V during the time interval t₁. During the time intervals t₂ and t₃, the timing signal A₂ is at a high logic level and, during this time period, the transmission gates TG2 is turned on. In this instance, the output terminal 92 is connected to the terminal 4V, and the segment signal C₁₂ ' has the potential of 4 V during the time intervals t₂ and t₃ as shown in FIG. 11. During the time interval t₄, the timing signal A₃ goes to a high logic level, rendering the transmission gate TG3 to turn on. In this instance, the output terminal 92 is coupled to the terminal 102 and, therefore, the segment drive signal C₁₂ ' has the potential of 2 V during the time interval t₄ as shown in FIG. 11. During the time intervals t₅ and t₆, the timing signal A₄ is at a high logic level and the output terminal 92 is coupled to the terminal 104. In this case, the segment drive signal C₁₂ ' has the potential of 0 during the time intervals t₅ and t₆ as shown in FIG. 11.

Transmission gates TG5 through TG8 of the switching circuit 89 are similar to those of the switching circuit 88 except that the inputs of the transmission gates TG5 through TG8 are connected to the terminals 104, 102, 100 and 102, respectively. Similarly, inputs of transmission of gates TG9 through TG12 are connected to the terminal 100, 102, 104 and 102, respectively. Output terminal 98 labelled C₀ ' is directly connected to the terminal 102 and, therefore, the potential of the segment drive signal C₀ ' is 2 V at all times as shown in FIG. 11. The switching circuits 89 and 90 will operate in the same manner as the switching circuit 88 and, therefore, the detailed description of the same is herein omitted for the sake of simplicity of description.

FIG. 28 shows an example of the segment driver 68 in which the decoder 66 is shown as connected to the logic circuit 60 through a level shifter 110 adapted to convert output signals from the logic circuit 60 to signal having voltage potentials 0 and 4 V. The decoder 66 generates two-bit signals d₁ and d₂, which are applied to control gates of first group of transmission gates TG15 through TG18 and a second group of transmission gates TG19 and TG20. Inputs of the transmission gates TG15 through TG18 are connected to the segment signal generator 88 to receive the segment signals C₁₂ ', C₁ ', C₀ ' and C₂, respectively. Outputs of the transmission gates TG15 and TG18 are connected together and coupled through lead 112 to input of the transmission gate TG19. Likewise, outputs of the transmission gates TG16 and TG17 are connected through lead 114 to an input of the transmission gate TG20. The outputs of the transmission gates TG19 and TG20 are coupled through lead 116 to a segment electrode 65a of the display device 65.

When the signal d₁ is at a high logic level, the transmission gates TG15 and TG16 are turned on, while the transmission gates TG17 and TG18 are turned off. If, on the contrary, the signal d₁ is at a low logic level, the transmission gates TG15 and TG16 are turned off, while the transmission gates TG17 and TG18 are turned on. On the other hand, if the signal d₂ is at a high logic level, the transmission gate TG19 is turned on, while the transmission gate TG20 is turned off. If, on the contrary, the signal d₂ is at a low logic level, the transmission gate TG19 is turned off, while the transmission gate TG20 is turned on.

When, now, both of the signals d₁ and d₂ go to a high logic level, the segment signal C₁₂ ' appears on lead 112 and the segment signal C₁ appears on lead 114. Since, in this instance, the transmission gate TG19 is turned on and the transmission gate TG20 is turned off, the segment signal C₁₂ ' is applied through lead 116 to the segment electrode 65a. When the signal d₁ goes to a low logic level while the signal d₂ is at a high logic level, the segment signal C₂ ' appears on lead 112 while the segment signal C₀ ' appears on lead 114. Since, in this case, the transmission gate TG19 is turned on and the transmission gate 20 is turned off, the segment signal C₂ ' is applied through lead 116 to the segment electrode 65a. In this manner, selected one of the segment drive signals are applied to the segment electrode 65a in dependence on the decoded outputs d₁ and d₂ delivered from the decoder 66.

FIG. 29 shows an example of the digit driver 62 shown in FIG. 23. The digit driver 62 comprises control terminals 120, 122, 124 and 126 labelled A₁, A₂, A₃ and A₄, and input terminals 128, 130 and 132 labelled 3 V, 2 V and V, respectively. The digit driver 62 also comprises a first group of transmission gates TG30 through TG33 and a second group of transmission gates TG34 through TG37. The transmission gates TG30 through TG33 have control gates connected to the control terminals 120 through 126, respectively, and inputs connected to terminals 128, 130, 132 and 130, respectively. Outputs of the transmission gates TG30 through TG33 are connected to the r₁ ' digit electrode. Similarly, the transmission gates TG34 through TG37 have control gates connected to the terminals 120, 122, 124 and 126, respectively, and inputs connected to the terminal 132, 130, 128 and 130, respectively. Outputs of the transmission gates TG34 through TG37 are connected to the r₂ digit electrode.

With this arrangement, when the timing signal A₁ goes to a high logic level, the transmission gates TG30 and TG34 are turned on and the remaining transmission gates are turnd off. Under these circumstances, the potential at the r₁ ' digit electrode is 3 V and the potential at the r₂ ' digit electrode is V. When the timing signal A₂ goes to a high logic level, the transmission gates TG31 and TG35 are turned on and the remaining transmission gates are turned off. Under these circumstances, the potential at the r₁ ' digit electrode is 2 V and the potential at the r₂ ' digit electrode is 2 V. When the timing signal A₃ goes to a high logic level, the transmission gates TG32 and TG36 are turned on and the potential at the r₁ digit electrode V while the potential at the r₂ ' digit electrode is 3 V. When the timing signal A₄ goes to a high logic level, the transmission gates TG33 and TG37 are turned on and the potential at the r₁ ' digit electrode is 2 V while the potential at the r₂ digit electrode is 2 V. In this manner, the potentials of the digit drive signals vary in dependence on the logic levels of the timing signals A₁ through A₄.

The brightness of a liquid crystal is a factor related to temperature. More specifically, the threshold voltage increases with a drop in temperture and decreases when the temperature rises. FIG. 30 shows the voltage characteristics for liquid crystal contrast. Reference numerals 200, 202 and 204 show temperatures of 25° C., 40° C. and 0° C. At 25° C., for example, an operation margin of √5 may suffice but over a wide temperature range such as 0° C. to 40° C. sufficient contrast is in general difficult to obtain. If the operation margin is widened, however, driving can be accomplished more readily over a wide temperature range and the liquid crystal itself performs a contrast temperature compensation. If in the V 1, V 2 range V 2/V 1 is chosen to be less than √7, contrast degradation due to temperature will not occur.

FIG. 31 shows voltage-contrast curves for a liquid crystal when driving is accomplished by the waveforms shown in FIG. 16. FIG. 31(1) shows a case in which a battery voltage of 1.6 Volts and a two-stage D.C. converter are employed. Accordingly, 2v 0=3.2 V, and 3V 0=4.8 V. In this case the liquid crystal threshold voltage V_(TH) is 1.3 Vrms, and the saturation voltage Vs is 3.4 Vrms. FIG. 31(2) shows a case where the battery voltage 2V 0 is 1.6 V. Thus, V 0=0.8 V, and 3 V 0=2.4 V. In such a case V_(TH) =0.65Vrms, and Vs=1.7Vrms.

FIG. 32 shows a general configuration for matrix driving according to the present method when n=2 and four potential levels are employed. FIG. 32(1) depicts states of potential levels. Here, a represents a 0 level, b an m level, c an m+1 level, and d a 2m+1 level. In other words, the potential difference between bc is 1, and the potential difference between ab and between cd is m. The potential levels between ab and between cd have been taken to be equal so that the DC component will not appear.

FIG. 32(2) depicts digit driving signals. With discussion limited to one-half period, the solid line represents a signal r₁ ' and the broken line a signal r₂ '. Reference numeral 206 denotes a portion where the potential levels of r₁ ' and r₂ ' coincide. Time intervals 208 and 210 are equal to each other. Since only a half-period will be considered, potentials b, c and d will be discussed. Here it suffices to impress the c potential upon the segment electrodes in order to bring both segments to a non-display state. That is, during the interval in which there is coincidence between the potential levels of the digit driving signals, it will suffice to apply a segment signal having the same potential level. In this case the rms voltage is m² +1/T. T is a given constant which is determined by a value of one-half of the frame time. For a case in which one segment at a matrix intersection is to be brought to a display state while the other segment at the intersection is to be brought to a non-display state, the rms voltage for the non-display state will be √{m² +(m+1)² ta+tb+m² td}/T if there is applied a segment signal which includes a, d levels for intervals 208 and 210 and a, b, c and d levels for the interval 206; here these intervals shall be denoted by ta, tb, tc and td. These intervals can be selected so that (m+1)² ta+tb+m² td=1. The rms voltage for the display state is given by √{(2m+1)hu 2+1+(m+1)² }/T.

When both segments are to be brought to a state of display, the rms voltage for the non-display state will be √{(2m+1)² +(m+1)² ta+tb+m² td+m² }/T if there is applied a segment signal which includes the a level for intervals other than that indicated at 206, and the a, b, c, and d levels for the interval 206, these intervals once again being denoted by ta, tb, tc and td. These intervals can be selected so that (m+1)² ta+tb+m² td+m² =(m+1)² +1. The rms voltage for the display state is given by √{(2m+1)² +(m+1)² +1}/T.

The waveforms shown in FIG. 16 indicates a case where n=2. In this case, the operation margin α is written as:

    α=√(5m.sup.2 +6m+3)/(m.sup.2 +1)=√7

If m is selected to be within a range between 0.51 and 7, the operation margin α may have a value greater than the maximum operation margin (√2+1) obtained in the prior art drive signals.

While the present invention has been shown and described with reference to particular examples, it should be noted that various other changes or modifications may be made without departing from the scope of the present invention. 

What is claimed is:
 1. A method of cyclically driving a liquid crystal display device having a matrix array of a first and second digit electrodes and a plurality of segment electrodes associated with said digit electrodes, respectively, to define a plurality of display elements, comprising the steps of:applying first and second digit drive signals to said first and second digit electrodes, respectively; and applying at least one of first, second and third segment drive signals to each of said plurality of segment electrodes, with the first segment drive signal inducing a state of non-display at said display elements on all of said digit electrodes during a half cycle period, the second segment drive signal inducing a state of display at said display elements on all of said digit electrodes during said half cycle period, and the third segment drive signal inducing a state of display at said display elements on one of said digit electrodes during said half cycle period; said first and second digit drive signals having first and second voltage potentials, respectively, during a first time interval of said half cycle period and having a third voltage potential serving as a reference potential during a second time interval of said half cycle period, said reference potential taking a value intermediate between said first and second voltage potentials, with a voltage difference between said first voltage potential of said first digit drive signal and said reference voltage potential being equal to that between said second voltage potential of said second digit drive signal during said first time interval and said first voltage potential of said digit drive signal being opposite in polarity to said second voltage potential of said second digit drive signal during said first time interval of said half cycle period; wherein said first segment drive signal has a potential level equal to said reference potential during said first and second time intervals, said second segment drive signal has the same potential as said reference potential during said first time interval and a fourth voltage potential largerin amplitude level than said first and second voltage potentials during said second time interval, and said third segment drive signal has at least one of said fourth voltage potential and a fifth voltage potential lower in amplitude level than said first and second voltage potentials during said first time interval and a voltage potential equal to said reference voltage potential during said second time interval.
 2. A method of cyclically driving a liquid crystal display device having a matrix array of first and second digit electrodes and a plurality of segment electrodes associated with said first and second digit electrodes, respectively, to define a plurality of display elements, comprising the steps of:applying first and second digit drive signals to said first and second digit electrodes, respectively; and applying at least one of first, second and third segment drive signals to each of said plurality of segment electrodes, with the first segment drive signal inducing a state of non-display at said display elements associated with said first and second digit electrodes during a half cycle period, the second segment drive signal inducing a state of display at all of said display elements on both of said first and second electrodes during said half cycle period, and the third segment drive signal inducing a state of display at said display elements on one of said first and second digit electrodes during said half cycle period; said first and second digit drive signals having first and second voltage potentials, respectively, during a first time interval of said half cycle period and having a reference potential during a second time interval of said half cycle period, said reference potential taking a value intermediate between said first and second voltage potentials, with a voltage difference between the first voltage potential of said first digit drive signal and said reference potential being equal to that between the second voltage potential of said second digit drive signal and said reference potential during said first time interval of said half cycle period and said first voltage potential of said first digit drive signal and said second voltage potential of said second digit drive signal being opposite in polarity to one another with respect to said reference potential during said first time interval of said half cycle period; wherein said first segment drive signal has a voltage potential equal to said reference potential during the first and second time intervals of said half cycle period, said second segment drive signal has a third voltage potential lower in amplitude level than said first and second voltage potentials during a prescribed time period of said first time interval and a fourth voltage potential larger in amplitude level than said first and second voltage potentials during another prescribed time period of said first time interval and during said second time interval, and the third segment drive signal has at least one of said third and fourth voltage potentials during the first interval and a voltage potential equal to said reference potential during said second time interval.
 3. A method of cyclically driving a liquid crystal display device having a matrix array of first and second digit electrodes and a plurality of segment electrodes associated with said first and second digit electrodes, respectively, to define a plurality of display elements, comprising the steps of:applying first and second digit drive signals to said first and second digit electrodes, respectively; and applying at least one of first, second and third segment drive signals to each of said plurality of segment electrodes, with the first segment drive signal inducing a state of non-display at said display elements associated with said first and second digit electrodes during a half cycle period, the second segment drive signal inducing a state of display at all of said display elements on both of said first and second digit electrodes during said half cycle period, and the third segment drive signal inducing a state of display at said display elements on one of said first and second digit electrodes during said half cycle period; said first and second digit drive signals having first and second voltage potentials, respectively, during a first time interval of said half cycle period and having a reference potential during a second time interval of said half cycle period, said reference potential taking a value intermediate between said first and second voltage potentials, said first and second digit drive signals having said second and first voltage potentials during a third time interval of said half cycle period, respectively, with a voltage difference between the first voltage potential of said first digit drive signal and said reference potential being equal to that between the second voltage potential of said second digit drive signal and said reference potential during said first time interval of said half cycle period and said first voltage potential of said first digit drive signal and said second voltage potential of said second digit drive signal being opposite in polarity to one another with respect to said reference potential during said first time interval of said half cycle period; wherein said first segment drive signal has a voltage potential equal to said reference potential during said first, second and third intervals of said half cycle period, said second segment drive signal has a third voltage potential lower in amplitude level than said first and second voltage potentials during said first, second and third time intervals, and said third segment drive signal has at least one of said first and third voltage potentials during said first, second and third time intervals.
 4. A method of cyclically driving a liquid crystal display device having a matrix array of first, second and third digit electrodes and a plurality of segment electrodes associated with said first and second digit electrodes, respectively, to define a plurality of display elements, comprising the steps of:applying first, second and third digit drive signals to said first, second and third digit electrodes, respectively; and applying at least one of first, second and third segment drive signals to each of said plurality of segment electrodes, with the first segment drive signal inducing a state of non-display at said display elements on said first, second and third digit electrodes during a half cycle period, the second segment drive signal inducing a state of display at said display elements on one of said first, second and third digit electrodes during said half cycle period, and the third segment drive signal inducing a state of display at said display elements on all of said first, second and third digit electrodes during said half cycle period; said first, second and third digit drive signals having first, second and third voltage potentials, respectively, during a first time interval of said half cycle period, said first and second digit drive signals having said third and first voltage potentials during a second time interval during which said third digit drive signal has said second voltage potential intermediate in amplitude between said first and third voltage potentials and serving as a reference potential, said second and third digit drive signals having said third and first voltage potentials, respectively, during a third time interval during which said first digit drive signal has said reference potential, said first, second and third digit drive signals having said reference potential during the remaining time intervals of said half cycle period; wherein said first segment drive signal has a voltage potential equal to said reference potential during said half cycle period, said second segment drive signal has one of said first, second and third voltage potentials during said first time interval and another one of said first, second and third voltage potentials during said second time interval, another one of said first, second and third voltage potentials during said third time intervals, and said reference potential during said remaining time intervals of said half cycle period, the third segment drive signal has said first voltage potential during said half cycle period. 